Just to check then, taking a calculated risk is not "skilled play"? (This will break the Poker analogy, but it is after all only an analogy.) And combat isn't "skilled play" (too much rolling dice and comparing the result to target numbers).
I don't understand what you are pressing towards.
Deciding (as one's PC) to jump over a pit to try and rescue a friend is taking a calculated risk. Enhancing the odds by putting on the boots worn by a recently-killed foe on the chance that they are Boots of Striding and Springing (suggested by the way the GM was narrating that foe in combat) would be layering a calculated risk (ie that the boots have the desired magical effect rather than, say, a curse) on top of the earlier calculated risk (ie that it is worth trying to make the jump to save one's friend). That is the sort of thing that I would anticipate being part of a "skilled play"/Gygaxian game.
If the Boots turn out to be magical, then there is a rule that tells us how far the wearer can jump and so the pit-crossing exercise is resolved deterministically. If the boots are not magical, then the attempt to jump over the pit will probably be resolved by a die roll (there being no general jumping rules in AD&D before Unearthed Arcana for thief-acrobats and barbarians, and then WSG for everyone else). Gygax's advice on this sort of thing is weak, but Moldvay's (in his Basic rules) is quite good.
The GM may or may not share the details of the die roll required before the player is required to commit to the jump - table practices on this are varied (and I don't think Moldvay makes it quite clear in his GMing advice). But that is secondary to the overall dynamics of the situation: the key thing is that the player is taking a chance with his/her character to try and rescue the other character, and (in choosing to put on the boots) is playing the fiction as part of that.
What I've just described is a real way to play D&D. I think three of the best exponents of it are Gygax (in his PHB, under the heading Successful Adventures just before the Appendices), from the player side but also giving ideas to GMs; Moldvay, in his Basic rulebook, who is writing from the GM side; and Lewis Pulsipher (writing in the late 70s/early 80s in White Dwarf), who writes from both player and GM sides.
I personally do not play in this style (i) because I don't find it super-interesting and (ii) as a GM I'm bad at it. That doesn't change the fact that it's a real approach to play. And the reason for calling it "skilled play" is simply that that is the label Gygax uses (or at least one of them - he also, in his PBH, refers to "playing well" by which he means this sort of engaging of the fiction).
Wargaming-style combat resolution - which is what AD&D and B/X use - is not an example of "skilled play" techniques in use. Obviously that sort of combat resolution can be quite exciting, which generates tensions in early D&D - should players stick to their skilled play priorities (eg Gygax advised avoiding wandering monsters if possible) or start fights because they're fun? Even in his DMG you can see Gygax flip-flopping a bit on the answer to this question, and by the time of 2nd ed AD&D we can see that "skilled play" priorities have been largely abandoned and it is assumed that from time to time the GM will frame the PCs into combat encounters because those are fun to play.
What about game mechanical attributes such as that mage hand can carry 10lbs. Relying on such values can be "skilled play", right? It is rolling the dice - taking a chance - that is verboten?
Again, I don't really understand what you are asking about. There is a fair bit of dice rolling in Gygaxian D&D - I quoted the rules on searching for secret doors not far upthread, and there are comparable rules for listening at doors, forcing doors open, etc.
In AD&D, if you are playing a fighter or cleric, it is obviously desirable - as far as character effectiveness is concerned - to acquire Gauntlets of Ogre Power, a Girdle of Giant Strength and a Hammer of Thunderbolts and become largely unstoppable in combat. But working this out isn't a manifestation of skilled play priorities. It's a manifestation of arithmetic ability. Conversely, a player who works out (what is not obvious to someone who hasn't read the books) that this combination of items
is apt to stack, because it's just like Thor, would be manifesting skilled play priorities - because it is reasoning about the fiction (in this case in a somewhat metagamey way).
4e D&D has a lot of character building options that are more intricate than the AD&D combo I described in the previous paragraph. Working out how to put them together can require fairly intricate arithmetic and optimising reasoning (eg by tracking which choices permit or exclude which other choices, and how those various permutations interact with other moving parts of the system like action economy and the like). That is obviously a manifestation of skill in the ordinary sense of the word, but has nothing to do with "skilled play" as Gygax uses that phrase. It's the same sort of skill that makes a person good at boardgames and mechanics-heavy wargames.
But there are obviously moments in 4e where players get to engage the fiction. In one of my 4e sessions a player had his wizard PC use Icy Terrain to freeze a puddle (or small pond - I can't remember all the details) so that someone-or-other could cross it without having to go through the water. That's the sort of thinking that does manifest skilled play priorities. If the carrying capacity of a mage hand - which is an element of the fiction, just like the iciness of Icy Terrain - mattered to some clever ploy, then that would also be a manifestation of skilled play priorities.
But while this sort of thing figured in my play of 4e, it wasn't the dominant priority. That is to say, the overall goal of play was not to solve and outwit the GM's challenges by coming up with clever, fiction-engaging solutions. Those were means to other ends. In Gygax's skilled play dungeoneering game they are really the end in themselves. (Yes, notionally, it's about treasure to earn XP, but Gygax is crystal clear that the conditions for accruing treasure should, exactly and precisely, be that the player solved and outwitted the GM's challenges by coming up with clever, fiction-engaging solutions!)